On Modeling of Lifetime Data Using One Parameter Akash, Lindley and Exponential Distributions

The time to the occurrence of event of interest is known as lifetime or survival time or failure time in reliability analysis. The event may be failure of a piece of equipment, death of a person, development (or remission) of symptoms of disease, health code violation (or compliance). The modeling and statistical analysis of lifetime data are crucial for statisticians and research workers in almost all applied sciences including engineering, medical science/biological science, insurance and finance, amongst others.

[1]  Benjamin Epstein,et al.  THE EXPONENTIAL DISTRIBUTION AND ITS ROLE IN LIFE TESTING , 1958 .

[2]  P. N. Lee,et al.  Survival Distributions: Reliability Applications in the Biomedical Sciences , 1976 .

[3]  H. Nadarajah,et al.  A Two-Parameter Lindley Distribution for Modeling Waiting and Survival Times Data , 2013 .

[4]  B. Efron.  Logistic Regression, Survival Analysis, and the Kaplan-Meier Curve , 1988 .

[5]  Faton Merovci,et al.  Transmuted Lindley Distribution , 2013 .

[6]  Rama Shanker,et al.  A quasi Lindley distribution , 2013 .

[7]  R. Shanker.  Akash Distribution and Its Applications , 2015 .

[8]  Edwin R. Fuller,et al.  Fracture mechanics approach to the design of glass aircraft windows: a case study , 1994, Optics & Photonics.

[9]  Hussain Ehtesham.  The Non-linear Functions of Order Statistics and their Properties in Selected Probability Models. , 2006 .

[10]  Gordon Johnston,et al.  Statistical Models and Methods for Lifetime Data , 2003, Technometrics.

[11]  David Lindley,et al.  Fiducial Distributions and Bayes' Theorem , 1958 .

[12]  Faton Merovci,et al.  A New Generalized Lindley Distribution , 2022, Journal of Statistics Applications & Probability Letters.

[13]  M Zelen,et al.  Estimation of exponential survival probabilities with concomitant information. , 1965, Biometrics.

[14]  Broderick O. Oluyede,et al.  A New Class of Generalized Power Lindley Distribution with Applications to Lifetime Data , 2016 .

[15]  Frank Proschan,et al.  Theoretical Explanation of Observed Decreasing Failure Rate , 2000, Technometrics.

[16]  Emilio Gómez-Déniz,et al.  The discrete Lindley distribution: properties and applications , 2011 .

[17]  M. E. Ghitany,et al.  Power Lindley distribution and associated inference , 2013, Comput. Stat. Data Anal..

[18]  Forrest W. BREY,et al.  Statistical Methods for Survival Data Analysis , 2003 .

[19]  Jorge Alberto Achcar,et al.  The Lindley distribution applied to competing risks lifetime data , 2011, Comput. Methods Programs Biomed..

[20]  Samir K. Ashour,et al.  Exponentiated power Lindley distribution , 2015, Journal of advanced research.

[21]  Francisco Louzada,et al.  An extended Lindley distribution , 2012 .

[22]  Dulal K. Bhaumik,et al.  Testing Parameters of a Gamma Distribution for Small Samples , 2009, Technometrics.

[23]  Sam C. Saunders,et al.  ESTIMATION FOR A FAMILY OF LIFE DISTRIBUTIONS WITH APPLICATIONS TO FATIGUE , 1969 .

[24]  Ali Dolati,et al.  Generalized Lindley Distribution , 2009 .

[25]  T. Bjerkedal.  Acquisition of resistance in guinea pigs infected with different doses of virulent tubercle bacilli. , 1960, American journal of hygiene.

[26]  Walter Zucchini,et al.  Model Selection , 2011, International Encyclopedia of Statistical Science.

[27]  D. J. Davis,et al.  AN ANALYSIS OF SOME FAILURE DATA , 1952 .

[28]  Rama Shanker,et al.  A two-parameter Lindley distribution , 2013, Statistics in Transition new series.

[29]  Richard L. Smith,et al.  A Comparison of Maximum Likelihood and Bayesian Estimators for the Three‐Parameter Weibull Distribution , 1987 .

[30]  U. Singh,et al.  The Truncated Lindley Distribution: Inference and Application , 2014 .

[31]  Frank Proschan.  Theoretical Explanation of Observed Decreasing Failure Rate , 2000, Technometrics.

[32]  Mavis Pararai,et al.  A Generalized Power Lindley Distribution with Applications , 2014 .

[33]  Umesh Singh,et al.  The inverse Lindley distribution: a stress-strength reliability model with application to head and neck cancer data , 2014, 1405.6268.

[34]  Broderick O. Oluyede,et al.  A new class of generalized Lindley distributions with applications , 2015 .

[35]  Rama Shanker,et al.  On Modeling of Lifetimes Data Using Exponential and Lindley Distributions , 2015 .

[36]  Elisa T. Lee,et al.  Statistical Methods for Survival Data Analysis , 1994, IEEE Transactions on Reliability.